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On the compactification of hyperconcave ends and the theorems of Siu-Yau and Nadel

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We show that the ‘pseudoconcave holes’ of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel’s theorems to dimension two.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    George Marinescu

  2. Institute of Mathematics, Romanian Academy, Bucharest, Romania

    George Marinescu

  3. Université Paris-Sud, Bâtiment 425-Mathématique, 91405, Orsay, France

    Tien-Cuong Dinh

Authors
  1. George Marinescu
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  2. Tien-Cuong Dinh
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Correspondence to George Marinescu or Tien-Cuong Dinh.

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Mathematics Subject Classification (1991)

32J05, 32C22, 53C55

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Marinescu, G., Dinh, TC. On the compactification of hyperconcave ends and the theorems of Siu-Yau and Nadel. Invent. math. 164, 233–248 (2006). https://doi.org/10.1007/s00222-005-0475-7

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  • DOI: https://doi.org/10.1007/s00222-005-0475-7

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